Anomalous diffusion limit for a kinetic equation with a thermostatted interface

IF 1.5 1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields Pub Date : 2023-12-29 DOI:10.1007/s00440-023-01251-3

引用次数: 0

Abstract

We consider the limit of solutions of scaled linear kinetic equations with a reflection-transmission-killing condition at the interface. Both the coefficient describing the probability of killing and the scattering kernel degenerate. We prove that the long-time, large-space limit is the unique solution of a version of the fractional in space heat equation that corresponds to the Kolmogorov equation for a symmetric stable process, which is reflected, or transmitted while crossing the interface and is killed upon the first hitting of the interface. The results of the paper are related to the work in Komorowski et al. (Ann Prob 48:2290–2322, 2020), where the case of a non-degenerate probability of killing has been considered.

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带有恒温界面的动力学方程的反常扩散极限

摘要我们考虑了在界面上具有反射-传输-杀伤条件的比例线性动力学方程的极限解。描述杀伤概率的系数和散射核均退化。我们证明了长时大空间极限是分数空间热方程版本的唯一解，该版本对应于对称稳定过程的科尔莫哥罗夫方程，该过程在穿越界面时被反射或传输，并在首次撞击界面时被杀死。本文的结果与 Komorowski 等人（Ann Prob 48:2290-2322, 2020 年）的研究成果相关，后者考虑了非退化杀伤概率的情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Probability Theory and Related Fields 数学-统计学与概率论

CiteScore

3.70

自引率

5.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Probability Theory and Related Fields publishes research papers in modern probability theory and its various fields of application. Thus, subjects of interest include: mathematical statistical physics, mathematical statistics, mathematical biology, theoretical computer science, and applications of probability theory to other areas of mathematics such as combinatorics, analysis, ergodic theory and geometry. Survey papers on emerging areas of importance may be considered for publication. The main languages of publication are English, French and German.